'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Applying this definition to our asset in some examples:- The total return, or performance over 5 years of ProShares Ultra Dow30 is 86.2%, which is lower, thus worse compared to the benchmark SPY (102%) in the same period.
- During the last 3 years, the total return, or increase in value is 26.9%, which is lower, thus worse than the value of 31.5% from the benchmark.

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Using this definition on our asset we see for example:- Looking at the annual return (CAGR) of 13.3% in the last 5 years of ProShares Ultra Dow30, we see it is relatively lower, thus worse in comparison to the benchmark SPY (15.1%)
- During the last 3 years, the annual return (CAGR) is 8.3%, which is lower, thus worse than the value of 9.6% from the benchmark.

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Which means for our asset as example:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the 30 days standard deviation of 40.6% of ProShares Ultra Dow30 is greater, thus worse.
- Compared with SPY (17.6%) in the period of the last 3 years, the 30 days standard deviation of 29.6% is greater, thus worse.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Which means for our asset as example:- Compared with the benchmark SPY (14.9%) in the period of the last 5 years, the downside volatility of 29.2% of ProShares Ultra Dow30 is greater, thus worse.
- Compared with SPY (12.4%) in the period of the last 3 years, the downside risk of 21% is larger, thus worse.

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Which means for our asset as example:- Compared with the benchmark SPY (0.6) in the period of the last 5 years, the Sharpe Ratio of 0.26 of ProShares Ultra Dow30 is smaller, thus worse.
- Compared with SPY (0.4) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.2 is smaller, thus worse.

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Applying this definition to our asset in some examples:- The ratio of annual return and downside deviation over 5 years of ProShares Ultra Dow30 is 0.37, which is lower, thus worse compared to the benchmark SPY (0.84) in the same period.
- During the last 3 years, the downside risk / excess return profile is 0.28, which is smaller, thus worse than the value of 0.57 from the benchmark.

'Ulcer Index is a method for measuring investment risk that addresses the real concerns of investors, unlike the widely used standard deviation of return. UI is a measure of the depth and duration of drawdowns in prices from earlier highs. Using Ulcer Index instead of standard deviation can lead to very different conclusions about investment risk and risk-adjusted return, especially when evaluating strategies that seek to avoid major declines in portfolio value (market timing, dynamic asset allocation, hedge funds, etc.). The Ulcer Index was originally developed in 1987. Since then, it has been widely recognized and adopted by the investment community. According to Nelson Freeburg, editor of Formula Research, Ulcer Index is “perhaps the most fully realized statistical portrait of risk there is.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Ulcer Ratio of 18 of ProShares Ultra Dow30 is greater, thus worse.
- During the last 3 years, the Ulcer Ratio is 17 , which is greater, thus worse than the value of 10 from the benchmark.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -63.1 days of ProShares Ultra Dow30 is smaller, thus worse.
- During the last 3 years, the maximum drop from peak to valley is -40.2 days, which is lower, thus worse than the value of -24.5 days from the benchmark.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs) in days.'

Using this definition on our asset we see for example:- Looking at the maximum days under water of 517 days in the last 5 years of ProShares Ultra Dow30, we see it is relatively higher, thus worse in comparison to the benchmark SPY (488 days)
- During the last 3 years, the maximum time in days below previous high water mark is 517 days, which is higher, thus worse than the value of 488 days from the benchmark.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Which means for our asset as example:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days below previous high of 146 days of ProShares Ultra Dow30 is greater, thus worse.
- Compared with SPY (177 days) in the period of the last 3 years, the average time in days below previous high water mark of 190 days is larger, thus worse.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares Ultra Dow30 are hypothetical and do not account for slippage, fees or taxes.